W can do 25% of a work in 30 days, X can do $\frac{1}{4}$ of the work in 10 days, Y can do 40% of the work in 40 days and Z can do $\frac{1}{3}$ of the work in 13 days. Who will complete the work first ?

The correct option is Z.

To determine who will complete the work first, we need to calculate the total number of days each person takes to complete 100% (or 1 whole part) of the work. The person who takes the fewest days will complete the work first.

Let's calculate the total time required for each person step-by-step:

1. For W:
W can do 25% of the work in 30 days.
To find the time taken for 100% of the work, we set up the relation:
Total days for W = 30 days × (100% / 25%)
Total days for W = 30 × 4 = 120 days.

2. For X:
X can do
$\frac{1}{4}$
of the work in 10 days.
To find the time taken for the whole work (1 unit):
Total days for X = 10 days × 4 = 40 days.

3. For Y:
Y can do 40% of the work in 40 days.
To find the time taken for 100% of the work:
Total days for Y = 40 days × (100% / 40%)
Total days for Y = 40 × 2.5 = 100 days.

4. For Z:
Z can do
$\frac{1}{3}$
of the work in 13 days.
To find the time taken for the whole work (1 unit):
Total days for Z = 13 days × 3 = 39 days.

Conclusion:
Comparing the total days taken by each person:
- W takes 120 days
- X takes 40 days
- Y takes 100 days
- Z takes 39 days

Since Z takes the minimum number of days (39 days) to complete the entire work, Z will complete the work first.